Sum of 4x^3+2x^2-4x+3 and 7x^3-4x+7x+8

Find the distance between the pair of parallel lines, y = x-11 & y = x-7

kenny6666 [7]

$k:\ y = x-11\ \ \ \Leftrightarrow\ \ \ x-y-11=0\\ and\\ l:\ y = x-7\ \ \ \Leftrightarrow\ \ \ x-y-7=0\\\\the\ distance:\\\\ d(k;l)= \frac{\big{|-11-(-7)|}}{\big{ \sqrt{1^2+1^2} }} =\frac{\big{|-11+7|}}{\big{ \sqrt{2} }} =\frac{\big{|-4|}}{\big{ \sqrt{2} }} =\frac{\big{4\cdot \sqrt{2} }}{\big{ \sqrt{2}\cdot \sqrt{2} }} =\frac{\big{4 \sqrt{2} }}{\big{2 }} =2 \sqrt{2}$

6 0

3 years ago

Read 2 more answers

Lee las situaciones y realiza lo siguiente con cada una:

Julli [10]

Answer:

Part 1) see the explanation

Part 2) see the explanation

Part 3) see the explanation

Part 4) see the explanation

Step-by-step explanation:

The question in English is

Read the situations and do the following with each one:

Write down the magnitudes involved

Write which magnitude is the independent variable and which is the dependent variable

It represents the function that describes the situation

SITUATIONS:

1) A machine prints 840 pages every 30 minutes.

2) An elevator takes 6 seconds to go up two floors.

3) A company rents a car at S/ 480 for 12 days.

4) 10 kilograms of papaya cost S/ 35

Part 1) we have

A machine prints 840 pages every 30 minutes

Let

x ----> the time in minutes (represent the variable independent or input value)

y ---> the number of pages that the machine print (represent the dependent variable or output value)

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In this problem

we have a a proportional variation

so

The value of the constant of proportionality is equal to

$k=\frac{y}{x}$

we have

$y=840\ pages\\x=30\ minutes$

substitute

$k=\frac{840}{30}=28\ pages/minute$

The linear equation is

$y=28x$

Part 2) we have

An elevator takes 6 seconds to go up two floors.

Let

x ----> the time in seconds (represent the variable independent or input value)

y ---> the number of floors (represent the dependent variable or output value)

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In this problem

we have a a proportional variation

so

The value of the constant of proportionality is equal to

$k=\frac{y}{x}$

we have

$y=2\ floors\\x=6\ seconds$

substitute

$k=\frac{2}{6}=\frac{1}{3}\ floors/second$

The linear equation is

$y=\frac{1}{3}x$

Part 3) we have

A company rents a car at S/ 480 for 12 days.

Let

x ----> the number of days (represent the variable independent or input value)

y ---> the cost of rent a car (represent the dependent variable or output value)

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In this problem

we have a a proportional variation

so

The value of the constant of proportionality is equal to

$k=\frac{y}{x}$

we have

$y=\$480\\x=12\ days$

substitute

$k=\frac{480}{12}=\$40\ per\ day$

The linear equation is

$y=40x$

Part 4) we have

10 kilograms of papaya cost S/ 35

Let

x ----> the kilograms of papaya (represent the variable independent or input value)

y ---> the cost (represent the dependent variable or output value)

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In this problem

we have a a proportional variation

so

The value of the constant of proportionality is equal to

$k=\frac{y}{x}$

we have

$y=\$35\\x=10\ kg$

substitute

$k=\frac{35}{10}=\$3.5\ per\ kg$

The linear equation is

$y=3.5x$

6 0

2 years ago

Any help if possible Thank you ❤

azamat

I believe it's 37CM, I had that question on my finals last year.

8 0

2 years ago

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PLEASEEE URGENT !!!!!!!!

xenn [34]

Answer:

Find the X and Y Intercepts 3x-5y=-20

Find the X and Y Intercepts 3x-5y=-20. 3x−5y=−20 3 x - 5 y = - 20. Find the x-intercepts. Tap for more steps

Step-by-step explanation:

5 0

2 years ago

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What is the domain and range of f(x)=2x^2+6x+2

lbvjy [14]

As is the case for any polynomial, the domain of this one is (-infinity, +infinity).

To find the range, we need to determine the minimum value that f(x) can have. The coefficients here are a=2, b=6 and c = 2,

The x-coordinate of the vertex is x = -b/(2a), which here is x = -6/4 = -3/2.

Evaluate the function at x = 3/2 to find the y-coordinate of the vertex, which is also the smallest value the function can take on. That happens to be y = -5/2, so the range is [-5/2, infinity).

3 0

2 years ago